and for the total remainder annex the figures cut off from the dividend to the remainder from the division. Divide 5,786,342 by 200. 200) 5786342 28931 with remainder 142. In this example, we cut off the two zeros at the right of the divisor and two figures at the right of the dividend; then we divide, putting the first figure of the quotient under the figure 8, which is the righthand figure of the first partial dividend when the entire divisor 200. is used. 70. The product of the divisor and quotient increased by the remainder is equal to the dividend. Hence, To test the accuracy of the work of division, find the product of the divisor and quotient, and to this product add the remainder; this result will be equal to the dividend if the work is correct. and Thus, in the last example, 200 × 28,931 = 5,786,200, 5,786,200+ 142 = 5,786,342 (the dividend). Divide by 20; by 30; and so on to 90. 1. There were 72 children in a Sunday-school, and they walked two and two to church. How many rows would they make? How many rows would there have been if they had walked three and three? 2. A boy had 97 filberts. He kept 34 for himself, and divided the rest equally among his 9 class-mates. How many did he give to each? 3. How many times must we take the number 7 to make 819? How many times the number 9? 4. Divide a paper of 264 pins equally into 8 papers. 5. 2691 poles were used in a certain hop-yard, and 3 were required for each plant. How many plants were there? 6. A blacksmith uses 7 nails in putting on one shoe, and in one day he used 336 nails. How many hoofs did he shoe? 7. A forest of 1995 trees is to be thinned by cutting down 1 tree in 7. How many will be taken out? 1 8. A regiment consists of 1200 men and 60 officers. How many men are there to each officer? 9. When beef is $7 per hundred-weight, how many hundred-weight can be bought for $9,700,327? 10. How many tons of coal, at $9, can be bought for $3,596,301? 11. A wagon travels 58,068 feet. How many times will a wheel 12 feet in circumference turn in going that distance? 12. A square yard contains 9 square feet. How many square yards in 3,917,502 square feet? 13. Aaron Reed left $325,645 for his wife and four children. How much had each, if the property was divided equally among them? 14. A grocer sells brown sugar at $9 per hundred-weight. If he receives $976,482, how many hundred-weight does he sell? 15. John Brown paid $375,008 for a tract of wild land, at $8 per acre. How many acres did he buy? 16. How many tons of coal, at $7 per ton, can be purchased for $3,785,908? 17. A merchant received $397,640 in selling a quantity of flour, at $8 per barrel. How many barrels did he sell? 18. What must be paid for 12 yards of cloth, if 5 yards cost $25? SOLUTION. If 5 yards cost $25, to find the cost of 1 yard $25 must be divided by 5; $25÷ 5 = $5, cost of 1 yard. 12 yards will cost 12 × $5 $60. Ans. 19. A drover paid $20 for 5 sheep. What will be the cost of 125 sheep? 20. Three cows cost $156. What must be paid for 27 cows? 21. If 7 tons of hay cost $105, what will be the cost of 63 tons? 22. If 9 barrels of flour are worth $63, how many barrels of apples, at $3 a barrel, will pay for 72 barrels of flour? 23. If 7 cords of birch wood are worth $28, how many cords of birch wood will pay for 6 barrels of sugar worth $16 a barrel? . 24. If 12 men do a piece of work in 12 hours, how many hours would it take 8 men to do the same work? LONG DIVISION. 71. The process of Long Division is the same as that of Short Division, except that the work is written in full, and the quotient is written over the dividend. Divide 41,668 by 78. The beginner will find it convenient to form a table of products of the divisor by the numbers 1, 2, 3,....., as follows: The third product is found by adding the first and second products, the fourth by adding the first and third, and so on. OPERATION. 538 78) 41998 390 299 As 78 is more than 41, it is necessary to take three figures of the dividend for the first partial dividend. Of the products in the table that do not exceed 419 the greatest is 390, that is, 5 x 78. Hence the first quotient figure is 5, and is written over the 9 in the dividend; then 390 is subtracted from 419. To the remainder 29, the next figure 9 of the dividend is annexed. Of the products that do not exceed 299, the greatest is 234, that is, 3 x 78. Hence 3 is the next figure of the quotient, and the next remainder is 65, to which the 8 of the dividend is annexed. Of the products that do not exceed 658, the greatest is 624, that is, 8 × 78. Hence the next figure of the quotient is 8, and the remainder 34. 234 658 624 34 remainder. After a little practice the operation of division can be performed without the aid of a table of products. Each quotient figure is estimated by taking for a trial divisor the left-hand figure of the divisor (or the left-hand figure in |